Kolmogorov–Arnold networks for turbulence anisotropy mapping
Bibliographic record
Abstract
This study evaluates the generalization performance and representation efficiency (parsimony) of a previously introduced Tensor Basis Kolmogorov–Arnold Network (TBKAN) architecture for data-driven turbulence modeling. The TBKAN framework replaces the multilayer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov–Arnold network (KAN), which reduces the model complexity while providing a structure that can be used with symbolic regression to provide potentially a physical interpretability that is not available in a “black box” MLP. While some prior work demonstrated TBKAN's feasibility for modeling a “simple” flat plate boundary layer flow, this study extends the TBKAN architecture to model more complex benchmark flows, in particular, square duct and periodic hills flows, which exhibit strong turbulence anisotropy, secondary motion, and flow separation and reattachment. A realizability-informed loss function is employed to constrain the model predictions, and, for the first time, TBKAN predictions are stably injected into the Reynolds-averaged Navier–Stokes equations to provide a posteriori predictions of the mean velocity field. Results show that a TBKAN achieves comparable or slightly improved accuracy relative to a TBNN (based on an MLP), while using fewer parameters to achieve this performance in comparison to a TBNN, both TBNN and TBKAN successfully capture key flow features in the square duct and periodic hills flows (e.g., secondary motions of the second kind, separation and reattachment zones, etc.) and demonstrate a significantly improved predictive performance relative to the conventional k–ω shear-stress transport turbulence closure model.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".